Since it's furring I'd use a finish nailer. You're going to run screws through it while doing the drywall so I wouldn't bother doing to much work to keep the furring in place. You need to have a screw into the joist 1/2". Do the math to figure out what length screw you'll need for your drywall. I'd bet a 1 5/8" would do you fine.

1/2 drywall + 1.5" 2x2 (maybe more), need at least a 2.5" screw. If the 2x2 isn't tight, the screw for the drywall may not catch right away and then it will jack the two apart. WIth a bead of construction adhesive there, it won't move. If you've got a nailer, then I'd forgo the screws, but still slap some glue up there.

Since it's furring I'd use a finish nailer. You're going to run screws through it while doing the drywall so I wouldn't bother doing to much work to keep the furring in place.

Tom

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I don't know anyone that uses 2.5" drywall screws, most are 1.25" so the furring strips must be securely attached to the rafter because the drywall screws aren't going to penetrate the actual rafter, just the furring strip unless of course you want to drop twice as much money on the extra long screws to do all the drywall with.

I guess I was thinking it would be cheaper to put 2x2s on than to sister with 2x6s. But perhaps the additional cost of screws, construction adhesive, my time, etc... isn't worth it. If I sister, I assume I can just nail it together, right?

However, If I sister them, I'm going to have nails from the roofing material getting in the way. Best to just pound them over? Or should I try to cut them off?

If you sister you're going to want to choose a smaller board like a 2x4. Given that you are attempting to add additional insulation I'd just go ahead with your furring out idea. It will be easier to acheive a better insulation result.

Sorry for sending you in another direction that perhaps isn't the best.

I'd glue and finish nail in your 2x2 furring. Then get some long screws to run your drywall with.

If the existing rafters aren't all nice and straight, you could straighten up the ceiling with some sisters. It would be possible with furring strips, but harder as each one may be different. Even if you used a 2x6, you want it to extend below the existing lumber, so it wouldn't have to go all the way to the roof decking. A 2x6 is in the order of 5.25-5.5" wide. The roofing nails probably don't stick too far through.